First part of sentence conveys a positive idea, therefore revered (choice A) would be best fit. The opening word "though" says, it is presenting something contrary to the rest of sentence. The other two words have a negative connotation. Vilified and slighted both mean to insult.

Second part of the sentence conveys the meaning that the officials want to discredit Socrates work, undermine (choice E) works best in the context.
One may challenge the work but that doesn't discredit the work. Acknowledge is the exact opposite of what the sentences are trying to convey

The first sentence presents a contrast. Since, the second half mentions threat, we need to have a positive word for the first blank - revered.

Since, the intent was to not completely destroy, but still have a negative impact, it was to undermine.